 So in this question it says that two boys A and B travel along the same path the displacement time graph for their journey is given in the following figure and we have to find out how far down the road has B traveled when A starts the journey okay so A is this line this is the graph for A and this is the displacement or distance time graph of B now clearly A starts late because you can see this A starts at A starts at T is equal to 4 second isn't it T is equal to 4 second now that means B would have already traveled for some distance in T equals to 4 second in so let's first find out velocity of A and B so velocity of or speed of A how to find out speed of anything is nothing but in a distance time graph you can find out by slope so let's draw the slope so let us take this point because this is easier okay so this is what is this this is 16 right so position is at 16 and this is right so this distance if you see is 16 okay and the time is 10 minus 4 that is 6 seconds so in 6 seconds right it travels A travels 16 meters so hence velocity of A is 16 upon 6 16 meters in how many seconds from 4 to 10 T is 4 and T is 10 so 10 minus 4 6 seconds so time taken is 6 seconds so it is 8 by 3 meter per second okay this is 8 by 3 meter per second velocity of B is how much we have to do again the slope thing so let's draw B B travels 16 meters in 10 seconds if you see B we take 10 seconds from the graph this is 10 is it B takes 10 seconds for the same 16 meters so 16 upon 10 which is 4 by not 4 by in fact 8 by 5 meter per second right 8 by 5 meter per second now so speeds are done so actually we are done with C so this is C and D what is the speed of B speed and velocity are same here because both of them are moving in the same direction without calculation the speed state who is traveling faster A or B oh so I missed this question actually so you can easily say who is faster moving faster A is moving faster so for this answer is B answer is A is moving faster A is moving faster we should have read the question once but anyways you can say A is moving faster because because st graph of A is having having more slope and we know that and we know that more the slope in st graph or distance time graph this is s and this is time this is T so in more the slope in st s t graph more is the speed okay so one A done I don't know how far the road has B traveled when A starts the journey so we have to find this out so let's find out A so in four seconds the if you if you if you see here already in four seconds this is a rough cut you can find out but then let's calculate it accurately so in four seconds how much B has traveled so in four second VB velocity of V into four second is the distance traveled by B in four seconds so which is VB how much is VB we just calculated 8 by 5 so 8 by 5 into 4 correct 8 by 5 into 4 that is 32 by 5 that is 6.4 meters right so you can see 6.4 roughly it is coming here here if you see this is nothing but let me draw this so this comes out to be around 6.4 right for 6.4 meters so three done A done B done C done and D also done are the speed of A and B uniform yes yes yes why slope is constant so answer is yes right because because both of them have both of them both of them have same slope same slope in respective respective s t graph this is the info okay so this is also done so both are uniform but they are not same they are not equal but they are uniform as in they have uniform velocity or constant velocity what does point X on graph represent so I have missed the graph this is point X okay so what is point X guys point X is nothing but point of meeting so that that is the point where they meet okay so point point where A and B A and B meet okay so A is faster B slower A started late so sometime after sometime A is going to cross B so that is the point now let's see this next question what is the speed of approach of A towards B so when is A approaching towards B when before 10 seconds A is approaching B and after 10 seconds A is separating from B is it it so before so let's write before P is equal to 10 seconds A is approaching B right E A approaches B approaches B A is moving towards B why because A is moving faster no so what will be the speed of approach simply V A minus B V this much will be the speed of approach relative velocity they are talking about so 8 by 3 minus 8 by 5 that means 8 common and 5 minus 3 2 by 15 so this is 16 by 15 meter per second so before T is equal to 10 seconds A approaches B with 16 by 15 meter per second and after P is equal to 10 seconds A separates A separates from B say A separates from B and obviously the magnitude of the separation velocity will be same V A minus B V with this velocity only it will be now moving away so again 8 by 3 minus 8 by 5 which is 16 upon 15 meter per second correct so this is velocity of approach and velocity of separation I hope you understood the entire question